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A268216
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Triangle read by rows: T(n,k) (n>=2, k=3..n+1) is the number of topologies t on n points having exactly k open sets such that t contains exactly one open set of size m for each m in {0,1,2,...,s,n} where s is the size of the largest proper open set in t.
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7
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2, 3, 6, 4, 12, 24, 5, 20, 60, 120, 6, 30, 120, 360, 720, 7, 42, 240, 840, 2520, 5040, 8, 56, 336, 1680, 6720, 20160, 40320, 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800
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OFFSET
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2,1
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LINKS
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Table of n, a(n) for n=2..46.
G. A. Kamel, Partial Chain Topologies on Finite Sets, Computational and Applied Mathematics Journal. Vol. 1, No. 4, 2015, pp. 174-179.
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EXAMPLE
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Triangle begins:
2;
3, 6;
4, 12, 24;
5, 20, 60, 120;
6, 30, 120, 360, 720;
7, 42, 240, 840, 2520, 5040;
8, 56, 336, 1680, 6720, 20160, 40320;
9, 72, 504, 3024, 15120, 60480, 181440, 362880;
10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800;
...
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MATHEMATICA
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i = 1; Table[Table[Binomial[n, i] FactorialPower[n - i, k], {k, 0, n - i - 1}], {n, 2, 9}] // Grid (* Geoffrey Critzer, Feb 19 2017 *)
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CROSSREFS
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Row sums give A038156. A008279 (main entry).
Triangles in this series: A268216, A268217, A268221, A268222, A268223.
Cf. A282507.
Sequence in context: A097275 A130879 A119741 * A346928 A245712 A285331
Adjacent sequences: A268213 A268214 A268215 * A268217 A268218 A268219
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, Jan 29 2016
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EXTENSIONS
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Definition clarified by Geoffrey Critzer, Feb 19 2017
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STATUS
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approved
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